Related papers: Some fast-growing tensor categories
We develop the theory of $\Theta$-positive representations from general Fuchsian groups to linear groups over real closed fields. Our definition, which does not assume the boundary map to be continuous, encompasses many generalizations of…
The principal aim of this note is to give an elementary proof of the fact that any two fiber functors of a Tannakian category are locally isomorphic. This builds on an idea of Deligne concerning scalar extensions of Tannakian categories and…
Restriction is a natural quasi-order on $d$-way tensors. We establish a remarkable aspect of this quasi-order in the case of tensors over a fixed finite field -- namely, that it is a well-quasi-order: it admits no infinite antichains and no…
We give a pedagogical survey of those aspects of the abstract representation theory of quantum groups which are related to the Tannaka-Krein reconstruction problem. We show that every concrete semisimple tensor *-category with conjugates is…
Category theory in homotopy type theory is intricate as categorical laws can only be stated "up to homotopy", and thus require coherences. The established notion of a univalent category (Ahrens, Kapulkin, Shulman) solves this by considering…
We classify braided tensor categories over C of exponential growth which are quasisymmetric, i.e., the squared braiding is the identity on the product of any two simple objects. This generalizes the classification results of Deligne on…
The main result of this paper may be stated as a construction of "almost representations" for the canonical presheaves of object extensions of length n on the C-systems defined by locally cartesian closed universe categories with binary…
We introduce a new method of constructing complete sequences of key polynomials for simple extensions of tame fields. In our approach the key polynomials are taken to be the minimal polynomials over the base field of suitably constructed…
Conformal algebras, recently introduced by Kac, encode an axiomatic description of the singular part of the operator product expansion in conformal field theory. The objective of this paper is to develop the theory of ``multi-dimensional''…
If a finitely generated torsion free group K has the property that all finitely generated subgroups S of K are either small or have growth constant bounded uniformly away from 1 then a non proper HNN extension G of K, that is a semidirect…
We give a Tannakian description for categories of l-adic perverse sheaves on semiabelian varieties which combines a construction of Gabber and Loeser for algebraic tori with a generic vanishing theorem for the cohomology of constructible…
A closed subgroup $G\subset_uU_N^+$ is called easy when its associated Tannakian category $C_{kl}=Hom(u^{\otimes k},u^{\otimes l})$ appears from a category of partitions, $C=span(D)$ with $D=(D_{kl})\subset P$, via the standard…
We show that finite quasisimple groups of Lie type in characteristic $p$ with an irreducible representation of prime degree $r$ over a finite field of characteristic $p$ have orders bounded above by a function of $r$, independent of $p$. We…
It has long been said that the theories of Galois and Tannakian categories over a field $k$ are just ``formally similar''. With this note I will argue that this is in fact not the case: not only do Tannakian categories generalize Galois…
We generalize one part of Thurston's hyperbolic Dehn filling theorem to arbitrary-rank semisimple Lie groups by showing that certain deformations of extended geometrically finite subgroups of a semisimple Lie group are still extended…
We study the semisimplification of the full karoubian subcategory generated by the irreducible finite dimensional representations of the algebraic supergroup $GL(m|n)$ over an algebraically closed field of characteristic zero. This…
The main contribution of this note is to establish a framework to extend results of tensor functions over specific field to general field. As a consequence of this framework, we extend the existing work to more general settings: \emph{(1)}…
We give an explicit characterization of solvable factors in factorizations of finite classical groups of Lie type. This completes the classification of solvable factors in factorizations of almost simple groups, finishing the program…
Recent developments in the theory of stability conditions and its relation to Teichmuller theory have revealed a deep connection between triangulated categories and surfaces. Motivated by this, we prove a categorical analogue of the…
For quantum theories with a classical limit (which includes the large N limits of typical field theories), we derive a hierarchy of evolution equations for equal time correlators which systematically incorporate corrections to the limiting…